The usage of a Crystalline Undulator (CU) has been identified as a promising solution for generating powerful and monochromatic $\gamma$-rays. A CU was fabricated at SSL through the grooving method, i.e., by the manufacturing of a series of periodical grooves on the major surfaces of a crystal. The CU was extensively characterized both morphologically via optical interferometry at SSL and structurally via X-ray diffraction at ESRF. Then, it was finally tested for channeling with a 400 GeV/c proton beam at CERN. The experimental results were compared to Monte Carlo simulations. Evidence of planar channeling in the CU was firmly observed. Finally, the emission spectrum of the positron beam interacting with the CU was simulated for possible usage in currently existing facilities.